The motion of a mass on a spring, with spring constant ${K}$ is as shown in figure. The equation of motion is given by $x(t)= A sin \omega t+ Bcos\omega t$ with $\omega=\sqrt{\frac{K}{m}}$ Suppose that at time $t=0$, the position of mass is $x(0)$ and velocity $v(0)$, then its displacement can also be represented as $x(t)=C \cos (\omega t-\phi)$, where $C$ and $\phi$ are

A block of mass $m$ is suspended separately by two different springs have time period $t_1$ and $t_2$ . If same mass is connected to parallel combination of both springs, then its time period will be

A $1 \,kg$ block attached to a spring vibrates with a frequency of $1\, Hz$ on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an $8\, kg$ block placed on the same table. So, the frequency of vibration of the $8\, kg$ block is ….. $Hz$

A particle of mass $200 \,gm$ executes $S.H.M.$ The restoring force is provided by a spring of force constant $80 \,N / m$. The time period of oscillations is …. $\sec$

A mass $M$ is suspended from a light spring. An additional mass m added displaces the spring further by a distance $x$. Now the combined mass will oscillate on the spring with period